I think it can vary a little depending on the assembly. Also, the new Detolfs don't have the hole in the wooden part etc so some tutorials are outdated.
My first lid -- a 15" window screen set -- worked until my ham piled up a bunch of toys and chewed out. I absolutely do not recommend that. Luckily, ham was recovered and then I had to make a lid ASAP for the night... so I came up with my current setup.
I ended up buying some 12" x 28" metal reptile screens, then attaching a 2" dowel on one side and a 1" dowel on the other. My inner width measurement was about 15". The dowels supporting the screen rest on the Detolf's inner bars, which I did not remove. The adhesive I used to attach the dowels to the reptile screen was a permanent adhesive strip because I didn't want to use a smelly glue.
This is a nice heavy lid and my ham has never escaped with this one on. I covered the sides with white duct tape to make them match the detolf lol.
I filled the gap in the middle with more dowel but there is still a little 1cm gap, so I don't put anything climbable there.
This was supposed to just be a temporary fix but tbh it has been working really well for me.
Not the classiest but I own no tools.